Vector sensors have been used in various underwater applications since the 1950's and typically contain individual transducers for measuring the acoustic pressure and the acoustic pressure-gradient at a single point in space. When the outputs of the transducers are combined in an additive format, cardioid beams are created and can be used to track sources of sound in water. Alternatively, when the outputs are combined in a multiplicative format, the acoustic intensity or acoustic impedance can be computed. In these ways, vector sensors have an inherent advantage over pressure sensors, particularly when used in direction finding applications and diagnostic measurement applications (e.g., acoustic intensity or impedance measurements).
The pressure transducer can take on many forms but usually consists of an air-backed hydrophone comprised of a piezoelectric disk or piezoelectric cylinder. The pressure-gradient transducer can also take on many forms but in many cases consists of a piezoelectric accelerometer contained within a rigid housing that also incorporates the pressure transducer. The use of an accelerometer to measure the pressure gradient is borne out of the linearized Euler equation that relates the pressure gradient to the particle acceleration in the acoustic medium (i.e., ∇p=−ρ0a, where p is the acoustic pressure, ρ0 is the ambient density of the medium, and a is the acoustic particle acceleration) in the same way Newton's second law relates force and acceleration on a body (i.e., F=ma, where F is the force, m is the mass of the body, and a is the acceleration). As such, this type of vector sensor relies on the “inertial principle” and moves in phase with the acoustic wave provided its dimensions are small in comparison to an acoustic wavelength.
The so-called buoyancy factor dictates the relative amplitude between the kinetic component of the acoustic wave and that of the vector sensor such that a neutrally buoyant sensor moves with the same amplitude as the acoustic wave, a positively buoyant sensor moves with a larger amplitude, and a negatively buoyant sensor moves with a lower amplitude. In this context, the buoyancy factor serves as a means to adjust the intrinsic sensitivity of the accelerometer (i.e., the frequency dependent sensitivity in units of V/g or V/m/s2 resulting from a calibration performed with a shaker and reference accelerometer) to the effective in-water acoustic sensitivity according to the relation β=(M0+Mi)/(Ms+Mi), where M0 is the displaced fluid mass based on the volume of the sensor, Ms is the mass of the sensor, and Mi is the induced fluid mass associated with the sensor translating in the acoustic medium during passage of a sound wave.
For a further discussion of the operating principles of inertial-type vector sensors, see, for example, J. A. McConnell, “Analysis of a Compliantly Suspended Acoustic Velocity Sensor,” J. Acoust. Soc. Am. 113(3), 1395-1405 (2003), or J. A. McConnell, “Development and Application of Inertial-Type Underwater Acoustic Intensity Probes,” Ph.D. Thesis, Ch. 2, 6, and 7, Pennsylvania State University, University Park, Pa. (2004), each incorporated by reference herein.